The thesis considers the action of the WI, and W2 wallpaper groups on a shape which is homeomorphic to the unit disc. A WI group is said to be optimal for a given shape if its action on the shape produces a packing which is at least as dense as any other WI packing. It is proved that for a given shape there must exist an optimal WI group. A set of necessary and sufficient conditions for a WI group to be optimal, for a given shape, are derived. An optimal W2 packing is defined in analogous manner. It is shown that for a given shape an optimal W2 group must exist. A set of necessary and sufficient conditions for a W2 group to be optimal, for a given shape, are derived. The thesis ends with conclusions and a number of suggestions for further work.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:536564 |
| Date | January 1991 |
| Creators | Sparks, Christopher |
| Publisher | University of Birmingham |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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